Hilbert Space Methods in Partial Differential Equations

Hilbert Space Methods in Partial Differential Equations
分享
扫描下方二维码分享到微信
打开微信,点击右上角”+“,
使用”扫一扫“即可将网页分享到朋友圈。
2010-03
ISBN: 0486474437 或 9780486474434
定价: 102.00
装帧: 平装
开本: 其他
页数: 224页
正文语种: 英语
  • This text surveys the principal methods of solving partial differential equations. Suitable for graduate students of mathematics, engineering, and physical sciences, it requires knowledge of advanced calculus.
    The initial chapter contains an elementary presentation of Hilbert space theory that provides sufficient background for understanding the rest of the book. Succeeding chapters introduce distributions and Sobolev spaces and examine boundary value problems, first- and second-order evolution equations, implicit evolution equations, and topics related to optimization and approximation. The text, which features 40 examples and 200 exercises, concludes with suggested readings and a bibliography.
                                     I. Elements of Hilbert Space   Linear Algebra   Convergence and Continuity   Completeness   Hilbert Space   Dual Operators; Identifications   Uniform Boundedness; Weak Compactness   Expansion in EigenfunctionsII. Distributions and Sobolev Spaces    Distributions    Sobolev Spaces    Trace    Sobolev's Lemma and Imbedding    Density and CompactnessIII. Boundary Value Problems      Introduction      Forms, Operators and Green's Formula      Abstract Boundary Value Problems      Examples      Coercivity; Elliptic Forms      Regularity      Closed operators, adjoints and eigenfunction expansionsIV. First Order Evolution Equations      Introduction      The Cauchy Problem      Generation of Semigroups      Accretive Operators; two examples      Generation of Groups; a wave equation      Analytic Semigroups      Parabolic EquationsV. Implicit Evolution Equations     Introduction     Regular Equations     Pseudoparabolic Equations     Degenerate Equations     ExamplesVI. Second Order Evolution Equations      Introduction      Regular Equations      Sobolev Equations      Degenerate Equations      ExamplesVII. Optimization and Approximation Topics       Dirichlet's Principle       Minimization of Convex Functions       Variational Inequalities       Optimal Control of Boundary Value Problems       Approximation of Elliptic Problems       Approximation of Evolution Equations   
  • 内容简介:
    This text surveys the principal methods of solving partial differential equations. Suitable for graduate students of mathematics, engineering, and physical sciences, it requires knowledge of advanced calculus.
    The initial chapter contains an elementary presentation of Hilbert space theory that provides sufficient background for understanding the rest of the book. Succeeding chapters introduce distributions and Sobolev spaces and examine boundary value problems, first- and second-order evolution equations, implicit evolution equations, and topics related to optimization and approximation. The text, which features 40 examples and 200 exercises, concludes with suggested readings and a bibliography.
  • 目录:

                                     I. Elements of Hilbert Space   Linear Algebra   Convergence and Continuity   Completeness   Hilbert Space   Dual Operators; Identifications   Uniform Boundedness; Weak Compactness   Expansion in EigenfunctionsII. Distributions and Sobolev Spaces    Distributions    Sobolev Spaces    Trace    Sobolev's Lemma and Imbedding    Density and CompactnessIII. Boundary Value Problems      Introduction      Forms, Operators and Green's Formula      Abstract Boundary Value Problems      Examples      Coercivity; Elliptic Forms      Regularity      Closed operators, adjoints and eigenfunction expansionsIV. First Order Evolution Equations      Introduction      The Cauchy Problem      Generation of Semigroups      Accretive Operators; two examples      Generation of Groups; a wave equation      Analytic Semigroups      Parabolic EquationsV. Implicit Evolution Equations     Introduction     Regular Equations     Pseudoparabolic Equations     Degenerate Equations     ExamplesVI. Second Order Evolution Equations      Introduction      Regular Equations      Sobolev Equations      Degenerate Equations      ExamplesVII. Optimization and Approximation Topics       Dirichlet's Principle       Minimization of Convex Functions       Variational Inequalities       Optimal Control of Boundary Value Problems       Approximation of Elliptic Problems       Approximation of Evolution Equations   
查看详情
系列丛书 / 更多
Hilbert Space Methods in Partial Differential Equations
Basic Algebra II:Second Edition
Nathan Jacobson 著
Hilbert Space Methods in Partial Differential Equations
One, Two, Three...Infinity:Facts and Speculations of Science
George Gamow 著
Hilbert Space Methods in Partial Differential Equations
Basic Algebra I:Second Edition
Nathan Jacobson 著
Hilbert Space Methods in Partial Differential Equations
Mathematics for the Nonmathematician
Morris Kline 著
Hilbert Space Methods in Partial Differential Equations
Dynamic Optimization, 2nd Edition
Morton I. Kamien 著
Hilbert Space Methods in Partial Differential Equations
The Thirteen Books of Euclid's Elements, Books 1 and 2
Euclid 著;Sir Thomas Heath 编
Hilbert Space Methods in Partial Differential Equations
Calculus of Variations
I. M. Gelfand 著
Hilbert Space Methods in Partial Differential Equations
The Thirteen Books of the Elements (Euclid, Vol. 2--Books III-IX):Books of Euclids Elements
Euclid 著;Thomas L.Heath 编
Hilbert Space Methods in Partial Differential Equations
Complex Variables,2nd Edition(Dover Books on Mathematics)
Stephen D.Fisher 著
Hilbert Space Methods in Partial Differential Equations
A Book of Abstract Algebra(second edition):Second Edition
Charles C. Pinter 著
Hilbert Space Methods in Partial Differential Equations
Ordinary Differential Equations
Morris、Harry Pollard 著
Hilbert Space Methods in Partial Differential Equations
Elements of the Theory of Functions and Functional Analysis
A.N.Kolmogorov、S.V.Fomin 著
您可能感兴趣 / 更多
Hilbert Space Methods in Partial Differential Equations
现代哲学倾向
Ralph Barton Perry
Hilbert Space Methods in Partial Differential Equations
实函数导论(第四版)(影印版)
Ralph、P.Boas 著
Hilbert Space Methods in Partial Differential Equations
复分析导引(第二版)(影印版)
Ralph P. Boas;Second
Hilbert Space Methods in Partial Differential Equations
沙丘的世界:风沙如何塑造行星景观
Ralph D. Lorenz 著;柳本立 译
Hilbert Space Methods in Partial Differential Equations
PenguinEssentials:InvisibleMan
Ralph Ellison 著
Hilbert Space Methods in Partial Differential Equations
RalphMasiello'sOceanDrawingBook
Ralph Masiello 著
Hilbert Space Methods in Partial Differential Equations
TwilightComesTwice
Ralph Fletcher 著;Kate Kiesler 绘
Hilbert Space Methods in Partial Differential Equations
EmersonSelectedJournals1841-1877
Ralph Waldo Emerson 著
Hilbert Space Methods in Partial Differential Equations
LifeCycleAssessment:Principles,PracticeandProspects
Ralph Horne 著
Hilbert Space Methods in Partial Differential Equations
SacredMushroomofVisions:Teonanacatl:ASourcebookonthePsilocybinMushroom
Ralph Metzner 编
Hilbert Space Methods in Partial Differential Equations
FlyingSolo
Ralph Fletcher 著
Hilbert Space Methods in Partial Differential Equations
TheCollectedEssaysofRalphEllison
Ralph Ellison、John Callahan 著